Does replacing a lost or stolen card count as opening a new account for credit scoring purposes?

It depends on whether or not you open a new account. Most of the time credit card companies transfer the account, keeping the starting date as the opening date of the account. The consumer is sent a new card, with a new number. The old account is notated "lost or stolen" and "transferred". If this is your situation, you are not taking a hit to your credit score.

If, on the other hand, you open the account yourself. You may get an inexperienced customer service rep who takes the wrong sequence of steps and performs both a "hard" inquiry and causes a new account to generate.

Either way, you will never lose the years of good history you have on the lost card account, but obviously, the first situation would be in your best interests. Call your credit card company and question them carefully about the procedure.